Since Max is wasting his time in his List I Communication credit lecture, he decided to start taking subsequences of arrays instead!

Specifically, he has ~N~ integers, ~A_i~, and wants to take a subsequence of length ~K~, but to make his life even harder, his List I Communication credit professor adds a restriction: he must find the subsequence that has a length of ~K~ with the minimum sum of the absolute difference between consecutive terms.

That is, he must minimize ~|B_1 - B_2| + |B_2 - B_3| + \dots + |B_{K-1} - B_K|~, where ~B_i~ is the ~i^\text{th}~ element of his subsequence and ~|A - B|~ denotes the absolute difference between ~A~ and ~B~.

Can you find the minimum sum of absolute differences for every possible subsequence of length ~K~?

Constraints

~2 \le N \le 50\,000~

~2 \le K \le \min(100, N)~

~1 \le A_i \le 50\,000~

Subtask 1 [40%]

~2 \le N \le 1\,000~

Subtask 2 [60%]

No additional constraints.

Input Specification

The first line will contain two integers, ~N~ and ~K~, the array's length and the subsequence's length, respectively.

The second line will contain ~N~ integers, ~A_i~, the elements of the array.

Output Specification

Output the minimum sum of absolute differences between consecutive elements for any subsequence of length ~K~.

Sample Input 1

6 2
1 5 6 2 1 3

Sample Output 1

0

Explanation for Sample 1

It can be proven that the minimal sum is achieved with the subsequence ~[A_1 = 1, A_5 = 1]~.

Sample Input 2

6 4
3 2 6 2 7 9

Sample Output 2

6

Explanation for Sample 2

It can be proven that the minimal sum is achieved with the subsequence ~[A_1 = 3, A_2 = 2, A_4 = 2, A_5 = 7]~.